Properties

Label 2.2.241.1-9.2-e
Base field \(\Q(\sqrt{241}) \)
Weight $[2, 2]$
Level norm $9$
Level $[9, 9, 248w + 1801]$
Dimension $14$
CM no
Base change no

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Base field \(\Q(\sqrt{241}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[9, 9, 248w + 1801]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $60$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{14} + 4x^{13} - 15x^{12} - 71x^{11} + 71x^{10} + 466x^{9} - 79x^{8} - 1388x^{7} - 195x^{6} + 1858x^{5} + 329x^{4} - 1005x^{3} - 77x^{2} + 120x + 13\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -393w - 2854]$ $...$
2 $[2, 2, -393w + 3247]$ $\phantom{-}e$
3 $[3, 3, 4w - 33]$ $...$
3 $[3, 3, 4w + 29]$ $\phantom{-}0$
5 $[5, 5, 42w + 305]$ $...$
5 $[5, 5, -42w + 347]$ $...$
29 $[29, 29, 1820w + 13217]$ $...$
29 $[29, 29, 1820w - 15037]$ $...$
41 $[41, 41, -80w - 581]$ $...$
41 $[41, 41, 80w - 661]$ $...$
47 $[47, 47, 34w - 281]$ $...$
47 $[47, 47, 34w + 247]$ $...$
49 $[49, 7, -7]$ $...$
53 $[53, 53, 6w + 43]$ $...$
53 $[53, 53, 6w - 49]$ $...$
59 $[59, 59, 10w + 73]$ $...$
59 $[59, 59, 10w - 83]$ $...$
61 $[61, 61, 4178w + 30341]$ $...$
61 $[61, 61, 4178w - 34519]$ $...$
67 $[67, 67, -332w + 2743]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, 4w + 29]$ $-1$